April 7th, 2013, 06:37 PM  #1 
Member Joined: Jan 2013 Posts: 54 Thanks: 0  Convergence and divergence
1. infinity E.........1/n n = 1 2. infinity E ........1/n^2 n = 1 The first series diverges and the second converges to pi^2/6. Somewhere between the two series, behaviour switches from divergence to convergence. Where is the dividing line? First, I don't get why the first series diverges and the second series converges. They are both approaching 0 but the second series is approaching it faster. Why is this so? 
April 8th, 2013, 12:56 AM  #2  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Convergence and divergence Quote:
Is the dividing line. Quote:
Quote:
 
April 8th, 2013, 03:41 AM  #3 
Math Team Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,989 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus  Re: Convergence and divergence [color=#000000] is divergent because . is convergent because .[/color] 
April 8th, 2013, 07:39 AM  #4 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: Convergence and divergence
By the ratio test, converges as long as so that "1" is the "dividing line". 

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